Simplify the following expression: $\dfrac{16q^5}{4q^2}$ You can assume $q \neq 0$.
Answer: $ \dfrac{16q^5}{4q^2} = \dfrac{16}{4} \cdot \dfrac{q^5}{q^2} $ To simplify $\frac{16}{4}$ , find the greatest common factor (GCD) of $16$ and $4$ $16 = 2 \cdot 2 \cdot 2 \cdot 2$ $4 = 2 \cdot 2$ $ \mbox{GCD}(16, 4) = 2 \cdot 2 = 4 $ $ \dfrac{16}{4} \cdot \dfrac{q^5}{q^2} = \dfrac{4 \cdot 4}{4 \cdot 1} \cdot \dfrac{q^5}{q^2} $ $\phantom{ \dfrac{16}{4} \cdot \dfrac{5}{2}} = 4 \cdot \dfrac{q^5}{q^2} $ $ \dfrac{q^5}{q^2} = \dfrac{q \cdot q \cdot q \cdot q \cdot q}{q \cdot q} = q^3 $ $ 4 \cdot q^3 = 4q^3 $